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# Barn - The"Barn Paradox A runner travelling at 0.75c is...

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The “Barn Paradox” A runner, travelling at 0.75c (!!), is carrying a long pole, which he knows to have length 15m. The pole is oriented in his direction of travel. He carries the pole as he passes through a barn, which has a length of 10 m. Straightforward . . . so what is the paradox? The length of the pole as measured by an observer who is stationary with respect to the ground is 9.9m. This is an application of “length contraction”. Thus, the pole seems shorter to the observer on the ground, because it is moving in his frame of reference. The length that he observes is L = L 0 15 / 1 . 51 9 . 9 m because γ = q 16 / 7 1 . 51 . Thus, according to the observer, when the runner enters the barn (whose length, measured with respect to the ground, is 10m), the pole should be able to fit inside! Now the paradox: The length of the barn as seen (measured) by the runner is 6.6m. This is again an example of “length contraction”. In the frame of reference of the runner, the barn is moving, so that its length is measured to be L B = L B 10 / 1 . 51 6 . 6 m How then can the pole fit inside? To explain, imagine that there are two doors to the barn, one for the entry, and one for the exit of the runner. (He is always running in a straight line.) At the beginning, the entry door is open, but the exit door is closed. Exactly at the time that the pole fits inside, the entry door closes, and the exit door opens, to allow the pole to pass through. These two events – closing the entry door and opening the exit door – happen, in this frame, at exactly the same time.

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Barn - The"Barn Paradox A runner travelling at 0.75c is...

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